source("./read_from_db.R")

This is a first pass exploration of different aspects of beer. The data was collected via the BreweryDB API. Special thanks to Kris Kroski for data ideation and co-membership in the honourable workplace beer consortium.

The main question this analysis is meant to tackle is: Are beer styles actually indicative of shared attributes of the beers within that style? Or are style boundaries more or less arbitrary? I took two approaches to this: unsupervised clustering and supervised prediction.

Clusters defined by the algorithm were compared to the style “centers” as defined by the mean ABV, IBU, and SRM. On the prediction side, predictor variables for include ABV (alcohol by volume), IBU (international bitterness units), SRM (a measure of color) as well as ingredients like hops and malts. The outcome variable is the style that beer was assigned.

This document starts off with an explanation of how I sourced beer data from BreweryDB, cleaned that data, and stuck the parts of it I wanted in a database. (These are just the highlights; the code actually executed in this document queries that database, specifically by sourcing the file read_from_db.R, also in this repo, rather than hitting the BreweryDB API. This is done for expediency’s sake as the code below detailing how to actually get the beer data, run in full in run_it.R, takes some time to execute.)

It then moves into clustering (k-means) and prediction (neural net, random forest).

The answer thus far seems to be that the beer landscape is more of a spectrum than a collection of neatly differentiated styles. Beer-intrinsic attributes like bitterness aren’t great predictors of style. The relative importance of different variables depeends on the prediction method used. However, one style-defined attribute, the glass a beer is served in, increased the accuracy of prediction substantially.

Of course, other important aspects of the flavor, body, smell, etc. of the beers could not be considered because this data is not available from BreweryDB.

Workflow Overview

Get and Prepare

When we first hit the BreweryDB API to iteratively pull in all beers and their ingredients along with other things we might want like breweries and glassware. Then we unnest the JSON responses, including all the ingredients columns, and dump this all into a MySQL database.

Next, we create a style_collapsed column to reduce the number of levels of our outcome variable. We do this by greping through each beer’s style to determine if that style contains a keyword that qualifies it to be rolled into a collapsed style; if it does, it gets that keyword in a style_collapsed column.

Finally we unnest the ingredients hops and malts into a wide, sparse dataframe. Individual ingredients are now columns, with each beer still in its own rows; a cell gets a 1 if ingredient is present and 0 otherwise. This allows more granual inference into ingredients’ effects on both style and bitterness (occasioning a short foray into hops).

Short foray into hops

A quick look at the most popular hops and an exploration of the relationship between hops and bitterness.

Infer

Cluster: unsupervised k-means clustering partitioning the entire dataset into ten clusters. Next, we cluster on a dataset composed of just five selected styles into five clusters.

We then attempt to predict predict either style or style_collapsed using a neural net and a random forest. The main predictors are ABV, IBU, SRM, total number of hops, and total number of malts. The glass a beer is served in is also considered. Finally,

Short Aside

The question of what should be a predictor variable for style is a bit murky here. What should be fair game for predicting style and what shouldn’t? Characteristics of a beer that are defined by its style would seem to be “cheating” in a way. The only “inputs” to a beer we have in our dataset are its ingredients, primarly hops and malts. While these certainly have an effect on its flavor profile, I consider them semi-cheating because if style is determined beforehand it likely determines at least in part which ingredients are added. The main candidates in my mind are ABV, IBU, and SRM. These are “outputs” of a beer (in the sense that they can only be exactly determined once a beer is brewered) that meaningfully define it. While correlated ABV is correlated with both IBU and SRM, the three are theoretically orthogonal to each other. A style-defined attribute like glass type is a bad candidate for a predictor variable because it is completely decoupled from the beer itself and determined entirely by the style the beer has been assigned to.

Get and Prepare Data

Getting beer, the age-old dilemma

The BreweryDB API returns a certain number of results per page; if we want
So, we hit the BreweryDB API and ask for 1:number_of_pages
- We can change number_of_pages to, e.g., 3 if we only want the first 3 pages
- If there’s only one page (as is the case for the glassware endpoint), numberOfPages won’t be returned, so in this case we set number_of_pages to 1
The addition parameter can be an empty string if nothing else is needed

base_url <- "http://api.brewerydb.com/v2"
key_preface <- "/?key="

paginated_request <- function(ep, addition, trace_progress = TRUE) {    
  full_request <- NULL
  first_page <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                , "&p=1"))
  number_of_pages <- ifelse(!(is.null(first_page$numberOfPages)), 
                            first_page$numberOfPages, 1)      

    for (page in 1:number_of_pages) {                               
    this_request <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                    , "&p=", page, addition),
                             flatten = TRUE) 
    this_req_unnested <- unnest_it(this_request)    #  <- request unnested here
    if(trace_progress == TRUE) {message(paste0("Page ", this_req_unnested$currentPage))}
    full_request <- bind_rows(full_request, this_req_unnested[["data"]])
  }
  return(full_request)
} 

all_beer_raw <- paginated_request("beers", "&withIngredients=Y")

Function for unnesting JSON used inside paginated_request() below
- Takes the column named name nested within a column in the data portion of the response
  - If the name column doesn’t exist, it takes the first nested column
We use something similar to unnest ingredient like all of a beer’s hops and malts into a long string contained in hops_name and malt_name

unnest_it <- function(df) {
  unnested <- df
  for(col in seq_along(df[["data"]])) {
    if(! is.null(ncol(df[["data"]][[col]]))) {
      if(! is.null(df[["data"]][[col]][["name"]])) {
        unnested[["data"]][[col]] <- df[["data"]][[col]][["name"]]
      } else {
        unnested[["data"]][[col]] <- df[["data"]][[col]][[1]]
      }
    }
  }
  return(unnested)
}

Collapse Styles

Save the most popular styles in keywords
Loop through each keyword
- For each beer, grep through its style column to see if it contains any one of these keywords
- If it does, give it that keyword in a new column style_collapsed
If a beer’s name matches multiple keywords, e.g., American Double India Pale Ale would match Double India Pale Ale, India Pale Ale, and Pale Ale, its style_collapsed is the last of those that appear in keywords
- This is why keywords are intentionally ordered from most general to most specific
- So in the case of an case of American Double India Pale Ale: since Double India Pale Ale appears in keywords after India Pale Ale and Pale Ale, an American Double India Pale Ale would get a style_collapsed of Double India Pale Ale
If no keyword is contained in style, style_collapsed is just whatever’s in style; in other words, it doesn’t get collpsed into a bigger bucket
- This isn’t a huge problem because we’ll pare down to just the most popular styles later, however we could think about creating a catchall “Other” level for style_collapsed

keywords <- c("Lager", "Pale Ale", "India Pale Ale", "Double India Pale Ale", "India Pale Lager", "Hefeweizen", "Barrel-Aged","Wheat", "Pilsner", "Pilsener", "Amber", "Golden", "Blonde", "Brown", "Black", "Stout", "Porter", "Red", "Sour", "Kölsch", "Tripel", "Bitter", "Saison", "Strong Ale", "Barley Wine", "Dubbel", "Altbier")

collapse_styles <- function(df, trace_progress = TRUE) {
  
  df[["style_collapsed"]] <- vector(length = nrow(df))
  
  for (beer in 1:nrow(df)) {
    if (grepl(paste(keywords, collapse="|"), df$style[beer])) {    
      for (keyword in keywords) {         
        if(grepl(keyword, df$style[beer]) == TRUE) {
          df$style_collapsed[beer] <- keyword    
        }                         
      } 
    } else {
      df$style_collapsed[beer] <- as.character(df$style[beer])       
    }
    if(trace_progress == TRUE) {message(paste0("Collapsing this ", df$style[beer], " to: ", df$style_collapsed[beer]))}
  }
  return(df)
}

Then we collapse further; right now we just combine all wheaty bears into Wheat and Pils-like beers into Pilsener (with two e’s) by fct_collapseing those levels

collapse_further <- function(df) {
  df[["style_collapsed"]] <- df[["style_collapsed"]] %>%
    fct_collapse(
      "Wheat" = c("Hefeweizen", "Wheat"),
      "Pilsener" = c("Pilsner", "American-Style Pilsener") # pilsener == pilsner == pils
    )
  return(df)
}

Split out Ingredients

When we unnested ingredients, we just concatenated all of the ingredients for a given beer into a long string. If we want, we can split out the ingredients that were concatenated in <ingredient>_name with this split_ingredients function.

This takes a vector of ingredients_to_split, so e.g. c("hops_name", "malt_name") and creates one column for each type of ingredient (hops_name_1, hops_name_2, etc.). It’s flexible enough to adapt if data in BreweryDB changes and a beer now has 15 hops where before the maximum number of hops a beer had was 10.

split_ingredients <- function(df, ingredients_to_split) {
  
  ncol_df <- ncol(df)
  
  for (ingredient in ingredients_to_split) {

    ingredient_split <- str_split(df[[ingredient]], ", ")    
    num_new_cols <- max(lengths(ingredient_split))    
  
    for (num in 1:num_new_cols) {
      
      this_col <- ncol_df + 1         
      
      df[, this_col] <- NA
      names(df)[this_col] <- paste0(ingredient, "_", num)
      ncol_df <- ncol(df)             
      for (row in seq_along(ingredient_split)) {          
        if (!is.null(ingredient_split[[row]][num])) {        
          df[row, this_col] <- ingredient_split[[row]][num]
        }
      }
      df[[names(df)[this_col]]] <- factor(df[[names(df)[this_col]]])
    }
    
    ncol_df <- ncol(df)
  }
  return(df)
}

Some quick summary stats on our main dataframe called beer_necessities:

dim(beer_necessities)

[1] 63495    39

str(beer_necessities)

'data.frame':   63495 obs. of  39 variables:
 $ id              : chr  "cBLTUw" "ZsQEJt" "tmEthz" "b7SfHG" ...
 $ name            : chr  "\"18\" Imperial IPA 2" "\"633\" American Pale Ale" "\"Admiral\" Stache" "\"Ah Me Joy\" Porter" ...
 $ description     : chr  "Hop Heads this one's for you!  Checking in with 143 IBU's this ale punches you in the mouth with extreme bitterness then rounds"| __truncated__ "Our first beer has been aptly named \"633\" after the Regions telephone exchange for starters.  \"If I could call a beer home, "| __truncated__ "Milwaukee Brewing Co’s take on a classic European style. Baltic Porters are the stronger lager fermented cousin of the classic "| __truncated__ "A robust porter style ale with a twist. This beer has moderate roastiness with a bitter finish, complemented by the sweetness o"| __truncated__ ...
 $ style           : Factor w/ 170 levels "Adambier","Aged Beer (Ale or Lager)",..: 13 20 30 139 23 108 8 20 7 54 ...
 $ abv             : num  11.1 6.33 7 5.4 4.8 4.6 8.5 5.8 7.6 10.8 ...
 $ ibu             : num  NA 25 23 51 12 NA 30 51 80 70 ...
 $ srm             : num  33 NA 37 40 NA 5 NA 8 NA NA ...
 $ glass           : Factor w/ 12 levels "Flute","Goblet",..: 6 NA 6 NA NA NA NA NA NA NA ...
 $ hops_name       : Factor w/ 969 levels "","#06300","Admiral, Aurora, Challenger, Fuggle (American), Target",..: NA NA 902 NA NA NA NA NA NA NA ...
 $ hops_id         : Factor w/ 969 levels "","1, 22, 23, 25, 146",..: NA NA 955 NA NA NA NA NA NA NA ...
 $ malt_name       : Factor w/ 923 levels "","Abbey Malt",..: NA NA 143 NA NA NA NA NA NA NA ...
 $ malt_id         : Factor w/ 923 levels "","165","165, 1947, 633, 1922",..: NA NA 124 NA NA NA NA NA NA NA ...
 $ glasswareId     : num  5 NA 5 NA NA NA NA NA NA NA ...
 $ styleId         : Factor w/ 170 levels "1","10","100",..: 109 89 7 82 106 101 102 89 107 68 ...
 $ style.categoryId: num  3 3 9 1 3 3 3 3 3 1 ...
 $ style_collapsed : Factor w/ 108 levels "Adambier","Altbier",..: 101 81 84 84 95 21 24 81 20 101 ...
 $ hops_name_1     : Factor w/ 113 levels "","#06300","Admiral",..: NA NA 90 NA NA NA NA NA NA NA ...
 $ hops_name_2     : Factor w/ 98 levels "Amarillo","Apollo",..: NA NA 70 NA NA NA NA NA NA NA ...
 $ hops_name_3     : Factor w/ 90 levels "Amarillo","Aramis",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_4     : Factor w/ 63 levels "Amarillo","Apollo",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_5     : Factor w/ 50 levels "Australian Dr. Rudi",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_6     : Factor w/ 29 levels "Cascade","Columbus",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_7     : Factor w/ 20 levels "Azzeca","Crystal",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_8     : Factor w/ 10 levels "Equinox","Experimental 06277",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_9     : Factor w/ 4 levels "Motueka","Nugget",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_10    : Factor w/ 4 levels "Nelson Sauvin",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_11    : Factor w/ 4 levels "Simcoe","Styrian Bobeks",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_12    : Factor w/ 3 levels "Summit","Super Galena",..: NA NA NA NA NA NA NA NA NA NA ...
 $ hops_name_13    : Factor w/ 2 levels "Target","Willamette": NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_1     : Factor w/ 128 levels "","Abbey Malt",..: NA NA 9 NA NA NA NA NA NA NA ...
 $ malt_name_2     : Factor w/ 134 levels "Amber Malt","Barley - Flaked",..: NA NA 64 NA NA NA NA NA NA NA ...
 $ malt_name_3     : Factor w/ 122 levels "Acidulated Malt",..: NA NA 73 NA NA NA NA NA NA NA ...
 $ malt_name_4     : Factor w/ 94 levels "Bamberg Smoked Malt",..: NA NA 52 NA NA NA NA NA NA NA ...
 $ malt_name_5     : Factor w/ 62 levels "Asheburne Mild Malt",..: NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_6     : Factor w/ 41 levels "Aromatic Malt",..: NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_7     : Factor w/ 19 levels "Barley - Roasted",..: NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_8     : Factor w/ 15 levels "Crisp 120","Crisp 77",..: NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_9     : Factor w/ 6 levels "Rye Malt","Smoked Malt",..: NA NA NA NA NA NA NA NA NA NA ...
 $ malt_name_10    : Factor w/ 1 level "Victory Malt": NA NA NA NA NA NA NA NA NA NA ...

Find the Most Popualar Styles

We find mean ABV, IBU, and SRM per collapsed style and arrange collapsed styles by the number of beers that fall into them. (This is of course dependent on how we collapse styles; if we looped all Double IPAs in with IPAs then the category IPA would be much bigger than it is if we keep the two separate.)

library(forcats)
# Pare down to only cases where style is not NA
beer_dat_pared <- beer_necessities[complete.cases(beer_necessities$style), ]
# Arrange beer dat by style popularity
style_popularity <- beer_dat_pared %>% 
  group_by(style) %>% 
  count() %>% 
  arrange(desc(n))
# Add a column that scales popularity
style_popularity <- bind_cols(style_popularity, 
                               n_scaled = as.vector(scale(style_popularity$n)))
# Find styles that are above a z-score of 0
popular_styles <- style_popularity %>% 
  filter(n_scaled > 0)
# Pare dat down to only beers that fall into those styles
popular_beer_dat <- beer_dat_pared %>% 
  filter(
    style %in% popular_styles$style
  ) %>% 
  droplevels() %>% 
  as_tibble()

How many rows do we have in our dataset of just beers that fall into the popular styles?

nrow(popular_beer_dat)

[1] 45871

Now we find the style centers.

# Find the centers (mean abv, ibu, srm) of the most popular styles
style_centers <- popular_beer_dat %>% 
  group_by(style_collapsed) %>% 
  add_count() %>% 
  summarise(
    mean_abv = mean(abv, na.rm = TRUE),
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_srm = mean(srm, na.rm = TRUE),
    n = median(n, na.rm = TRUE)          # Median here only for summarise. Should be just the same as n
  ) %>% 
  arrange(desc(n)) %>% 
  drop_na() %>% 
  droplevels()
# Give some nicer names
style_centers_rename <- style_centers %>% 
  rename(
    `Collapsed Style` = style_collapsed,
    `Mean ABV` = mean_abv,
    `Mean IBU` = mean_ibu,
    `Mean SRM` = mean_srm,
    `Numer of Beers` = n
  )

Take a look at the table, ordered by number of beers in that style, descending.

kable(style_centers_rename)

Collapsed Style	Mean ABV	Mean IBU	Mean SRM	Numer of Beers
India Pale Ale	6.578468	66.04268	9.989313	6524
Pale Ale	5.695480	40.86930	8.890306	4280
Stout	7.991841	43.89729	36.300000	4238
Wheat	5.158040	17.47168	5.861842	3349
Double India Pale Ale	8.930599	93.48142	11.006873	2525
Red	5.742565	33.81127	16.178862	2521
Lager	5.453718	30.64361	8.457447	2230
Saison	6.400189	27.25114	7.053476	2167
Blonde	5.595298	22.39432	5.625000	2044
Porter	6.182049	33.25369	32.197605	1973
Brown	6.159212	32.21577	23.592000	1462
Pilsener	5.227593	33.51346	4.413462	1268
Specialty Beer	6.446402	33.77676	15.520548	1044
Bitter	5.322364	38.28175	12.460526	939
Fruit Beer	5.195222	19.24049	8.666667	905
Herb and Spice Beer	6.621446	27.77342	18.166667	872
Sour	6.224316	18.88869	10.040816	797
Strong Ale	8.826425	36.74233	22.547945	767
Tripel	9.029775	32.51500	7.680556	734
Black	6.958714	65.50831	31.080000	622
Barley Wine	10.781600	74.04843	19.561404	605
Kölsch	4.982216	23.37183	4.371795	593
Barrel-Aged	9.002506	39.15789	18.133333	540
Other Belgian-Style Ales	7.516318	37.55812	17.549020	506
Pumpkin Beer	6.712839	23.48359	17.918033	458
Dubbel	7.509088	25.05128	22.940000	399
Scotch Ale	7.620233	26.36909	24.222222	393
German-Style Doppelbock	8.045762	28.88692	25.696970	376
Fruit Cider	6.205786	25.60000	12.000000	370
German-Style Märzen	5.746102	25.63796	14.322581	370

Ingredients

To get more granular with ingredients, we can split out each individual ingredient into its own column. If a beer or style contains that ingredient, its row gets a 1 in that ingredient column and a 0 otherwise.

From this, we can find the total number of hops and malts per grouper.

The dataframe we’ll use will be beer_necessities
This function takes a dataframe and two other parameters set at the outset:
- ingredient_want: this can be hops, malt, or other ingredients like yeast if we pull that in
- grouper: can be a vector of one or more things to group by, like beer name or style

pick_ingredient_get_beer <- function (ingredient_want, df, grouper) {
  
  # ----------------------- Setup --------------------------- #
  # We've already split ingredient number names out from the concatenated string into columns like `malt_name_1`,
  # `malt_name_2`, etc. We need to find the range of these columns; there will be a different number of malt
  # columns than hops columns, for instance. The first one will be `<ingredient>_name_1` and from this we can find
  # the index of this column in our dataframe. We get the name of last one with the `get_last_ing_name_col()`
  # function. Then we save a vector of all the ingredient column names in `ingredient_colnames`. It will stay
  # constant even if the indices change when we select out certain columns. 
  
  # First ingredient
  first_ingredient_name <- paste(ingredient_want, "_name_1", sep="")
  first_ingredient_index <- which(colnames(df)==first_ingredient_name)
  
  # Get the last ingredient
  get_last_ing_name_col <- function(df) {
    for (col in names(df)) {
      if (grepl(paste(ingredient_want, "_name_", sep = ""), col) == TRUE) {
        name_last_ing_col <- col
      }
    }
    return(name_last_ing_col)
  }
  
  # Last ingredient
  last_ingredient_name <- get_last_ing_name_col(df)
  last_ingredient_index <- which(colnames(df)==last_ingredient_name)
  
  # Vector of all the ingredient column names
  ingredient_colnames <- names(df)[first_ingredient_index:last_ingredient_index]
  
  # Non-ingredient column names we want to keep
  to_keep_col_names <- c("id", "cluster_assignment", "name", "abv", "ibu", "srm", "style", "style_collapsed")
  
  # -------------------------------------------------------------------------------# 
  
  # Inside `gather_ingredients()` we take out superflous column names that are not in `to_keep_col_names` or one 
  # of the ingredient columns, find what the new ingredient column indices are, since they'll have changed after 
  # we pared down and then gather all of the ingredient columns (e.g., `hops_name_1`) into one long column, 
  # `ing_keys` and all the actual ingredient names (e.g., Cascade) into `ing_names`.
  
  # ----------------------------- Gather columns --------------------------------- #
  gather_ingredients <- function(df, cols_to_gather) {
    to_keep_indices <- which(colnames(df) %in% to_keep_col_names)
    
    selected_df <- df[, c(to_keep_indices, first_ingredient_index:last_ingredient_index)]
    
    new_ing_indices <- which(colnames(selected_df) %in% cols_to_gather)    # indices will have changed since we pared down 
    
    df_gathered <- selected_df %>%
      gather_(
        key_col = "ing_keys",
        value_col = "ing_names",
        gather_cols = colnames(selected_df)[new_ing_indices]
      ) %>%
      mutate(
        count = 1
      )
    return(df_gathered)
  }
  beer_gathered <- gather_ingredients(df, ingredient_colnames)  # ingredient colnames defined above function
  # ------------------------------------------------------------------------------- # 
  
  # Next we get a vector of all ingredient levels and take out the one that's an empty string and 
  # use this vector of ingredient levels in `select_spread_cols()` below
  # Get a vector of all ingredient levels
  beer_gathered$ing_names <- factor(beer_gathered$ing_names)
  ingredient_levels <- levels(beer_gathered$ing_names) 
  
  # Take out the level that's just an empty string
  to_keep_levels <- !(c(1:length(ingredient_levels)) %in% which(ingredient_levels == ""))
  ingredient_levels <- ingredient_levels[to_keep_levels]
  
  beer_gathered$ing_names <- as.character(beer_gathered$ing_names)
  
  # ----------------------------------------------------------------------------- # 
  
  # Then we spread the ingredient names: we take what was previously the `value` in our gathered dataframe, the
  # actual ingredient names (Cascade, Centennial) and make that our `key`; it'll form the new column names. The
  # new `value` is `value` is count; it'll populate the row cells. If a given row has a certain ingredient, it
  # gets a 1 in the corresponding cell, an NA otherwise. 
  # We add a unique idenfitier for each row with `row`, which we'll drop later (see [Hadley's SO
  # comment](https://stackoverflow.com/questions/25960394/unexpected-behavior-with-tidyr)).
  
  # ------------------------------- Spread columns -------------------------------- #
  spread_ingredients <- function(df) {
    df_spread <- df %>% 
      mutate(
        row = 1:nrow(df)        # Add a unique idenfitier for each row which we'll need in order to spread; we'll drop this later
      ) %>%                                 
      spread(
        key = ing_names,
        value = count
      ) 
    return(df_spread)
  }
  beer_spread <- spread_ingredients(beer_gathered)
  # ------------------------------------------------------------------------------- # 
  
  # ------------------------- Select only certain columns ------------------------- #
  select_spread_cols <- function(df) {
    to_keep_col_indices <- which(colnames(df) %in% to_keep_col_names)
    to_keep_ingredient_indices <- which(colnames(df) %in% ingredient_levels)
    
    to_keep_inds_all <- c(to_keep_col_indices, to_keep_ingredient_indices)
    
    new_df <- df %>% 
      select_(
        .dots = to_keep_inds_all
      )
    return(new_df)
  }
  beer_spread_selected <- select_spread_cols(beer_spread)
  # ------------------------------------------------------------------------------- # 
  # Take out all rows that have no ingredients specified at all
  inds_to_remove <- apply(beer_spread_selected[, first_ingredient_index:last_ingredient_index], 
                          1, function(x) all(is.na(x)))
  beer_spread_no_na <- beer_spread_selected[ !inds_to_remove, ]
  
  
  # ----------------- Group ingredients by the grouper specified ------------------- #
  # Then we do the final step and group by the groupers.
  
  get_ingredients_per_grouper <- function(df, grouper = grouper) {
    df_grouped <- df %>%
      ungroup() %>% 
      group_by_(grouper)
    
    not_for_summing <- which(colnames(df_grouped) %in% to_keep_col_names)
    max_not_for_summing <- max(not_for_summing)
    
    browser()
    per_grouper <- df_grouped %>% 
      select(-c(abv, ibu, srm)) %>%    # taking out temporarily
      summarise_if(
        is.numeric,              
        sum, na.rm = TRUE
        # -c(abv, ibu, srm)
      ) %>%
      mutate(
        total = rowSums(.[(max_not_for_summing + 1):ncol(.)], na.rm = TRUE)    
      )
    
    # Send total to the second position
    per_grouper <- per_grouper %>% 
      select(
        id, total, everything()
      )
    
    # Replace total column with more descriptive name: total_<ingredient>
    names(per_grouper)[which(names(per_grouper) == "total")] <- paste0("total_", ingredient_want)
    
    return(per_grouper)
  }
  # ------------------------------------------------------------------------------- # 
  
  ingredients_per_grouper <- get_ingredients_per_grouper(beer_spread_selected, grouper)
  return(ingredients_per_grouper)
}

Now run the function with ingredient_want as first hops, then malt
Then join the resulting dataframes and remove/reorder some columns

# Same for malt
ingredients_per_beer_malt <- pick_ingredient_get_beer(ingredient_want = "malt", 
                                                      beer_necessities, 
                                                      grouper = c("id"))

Called from: get_ingredients_per_grouper(beer_spread_selected, grouper)
debug at #137: per_grouper <- df_grouped %>% select(-c(abv, ibu, srm)) %>% summarise_if(is.numeric, 
    sum, na.rm = TRUE) %>% mutate(total = rowSums(.[(max_not_for_summing + 
    1):ncol(.)], na.rm = TRUE))
debug at #149: per_grouper <- per_grouper %>% select(id, total, everything())
debug at #155: names(per_grouper)[which(names(per_grouper) == "total")] <- paste0("total_", 
    ingredient_want)
debug at #157: return(per_grouper)

# Join those on our original dataframe by name
beer_ingredients_join_first_ingredient <- left_join(beer_necessities, ingredients_per_beer_hops,
                                                    by = "id")
beer_ingredients_join <- left_join(beer_ingredients_join_first_ingredient, ingredients_per_beer_malt,
                                   by = "id")
# Take out some unnecessary columns
unnecessary_cols <- c("styleId", "abv_scaled", "ibu_scaled", "srm_scaled", 
                      "hops_id", "malt_id", "glasswareId", "style.categoryId")
beer_ingredients_join <- beer_ingredients_join[, (! names(beer_ingredients_join) %in% unnecessary_cols)]

Now we’re left with something of a sparse matrix of all the ingredients compared to all the beers

kable(beer_ingredients_join[1:20, ])

id	name	total_hops	total_malt	style	abv	ibu	srm	glass	hops_name	malt_name	style_collapsed	Cascade	Perle (American)	Saaz (American)	Sterling	Barley - Malted	Chocolate Malt	Honey Malt	Munich Malt	Oats - Flaked	Two-Row Pale Malt
cBLTUw	"18" Imperial IPA 2	0	0	American-Style Imperial Stout	11.10	NA	33	Pint	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
ZsQEJt	"633" American Pale Ale	0	0	American-Style Pale Ale	6.33	25.0	NA	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
tmEthz	"Admiral" Stache	2	4	Baltic-Style Porter	7.00	23.0	37	Pint	Perle (American), Saaz (American)	Barley - Malted, Chocolate Malt, Munich Malt, Oats - Flaked	Porter	0	1	1	0	1	1	0	1	1	0
b7SfHG	"Ah Me Joy" Porter	0	0	Robust Porter	5.40	51.0	40	NA	NA	NA	Porter	0	0	0	0	0	0	0	0	0	0
zcJMId	"Alternating Currant" Sour	0	0	American-Style Sour Ale	4.80	12.0	NA	NA	NA	NA	Sour	0	0	0	0	0	0	0	0	0	0
UM8GL6	"B" Street Pineapple Blonde	0	0	Golden or Blonde Ale	4.60	NA	5	NA	NA	NA	Blonde	0	0	0	0	0	0	0	0	0	0
NIaY9C	"B.B. Rodriguez" Double Brown	0	0	American-Style Brown Ale	8.50	30.0	NA	NA	NA	NA	Brown	0	0	0	0	0	0	0	0	0	0
PBEXhV	"Bison Eye Rye" Pale Ale \| 2 of 4 Part Pale Ale Series	0	0	American-Style Pale Ale	5.80	51.0	8	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
wRmmdv	"California Crude" Black IPA	0	0	American-Style Black Ale	7.60	80.0	NA	NA	NA	NA	Black	0	0	0	0	0	0	0	0	0	0
EPYNpW	"C’est Noir" Imperial Stout	0	0	British-Style Imperial Stout	10.80	70.0	NA	NA	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
AXmvOd	"Dust Up" Cloudy Pale Ale \| 1 of 4 Part Pale Ale Series	0	0	American-Style Pale Ale	5.40	54.0	11	NA	NA	NA	Pale Ale	0	0	0	0	0	0	0	0	0	0
c5pZg5	"EVL1" Imperial Red Ale	0	0	Imperial Red Ale	10.40	64.0	NA	NA	NA	NA	Red	0	0	0	0	0	0	0	0	0	0
xBKAka	"Galactic Wrath" IPA	0	0	American-Style India Pale Ale	7.50	75.0	NA	NA	NA	NA	India Pale Ale	0	0	0	0	0	0	0	0	0	0
Hr5A0t	"God Country" Kolsch	0	0	German-Style Kölsch / Köln-Style Kölsch	5.60	28.2	5	NA	NA	NA	Kölsch	0	0	0	0	0	0	0	0	0	0
UjFyXJ	"Hey Victor" Smoked Porter	0	0	Smoke Beer (Lager or Ale)	5.50	NA	NA	NA	NA	NA	Lager	0	0	0	0	0	0	0	0	0	0
5UcMBc	"Ignition" IPA	0	0	American-Style India Pale Ale	6.60	45.0	NA	Pint	NA	NA	India Pale Ale	0	0	0	0	0	0	0	0	0	0
mrVjY4	"Jemez Field Notes" Golden Lager	0	0	Golden or Blonde Ale	4.90	20.0	5	NA	NA	NA	Blonde	0	0	0	0	0	0	0	0	0	0
54rSgo	"Jemmy Dean" Breakfast Stout	0	0	Sweet or Cream Stout	NA	NA	NA	Pint	NA	NA	Stout	0	0	0	0	0	0	0	0	0	0
JsKjkk	"Mauvaises Choses"	0	0	Belgian-Style Pale Strong Ale	7.00	30.0	NA	Tulip	NA	NA	Strong Ale	0	0	0	0	0	0	0	0	0	0
b7WWL6	"Mike Saw a Sasquatch" Session Ale	2	2	Golden or Blonde Ale	4.70	26.0	NA	Pint	Cascade, Sterling	Honey Malt, Two-Row Pale Malt	Blonde	1	0	0	1	0	0	1	0	0	1

Now that the munging is done, onto the main question: do natural clusters in beer align with style boundaries?

Unsupervised Clustering

We K-means cluster beers based on certain numeric predictor variables.

Prep

Write a funciton that takes a dataframe, a set of predictors, a response variable, and the number of cluster centers you want
- NB: There are not not very many beers have SRM so we may not want to omit based on it
Take out missing values, and scale the data
Take out outliers, defined as beers have to have an ABV between 3 and 20 and an IBU less than 200
Then cluster on just the predictors and compare to the response variable

library(NbClust)
cluster_it <- function(df, preds, to_scale, resp, n_centers) {
  df_for_clustering <- df %>%
    select_(.dots = c(response_vars, cluster_on)) %>%
    na.omit() %>%
    filter(
      abv < 20 & abv > 3
    ) %>%
    filter(
      ibu < 200
    )
  df_all_preds <- df_for_clustering %>%
    select_(.dots = preds)
  df_preds_scale <- df_all_preds %>%
    select_(.dots = to_scale) %>%
    rename(
      abv_scaled = abv,
      ibu_scaled = ibu,
      srm_scaled = srm
    ) %>%
    scale() %>%
    as_tibble()
  df_preds <- bind_cols(df_preds_scale, df_all_preds[, (!names(df_all_preds) %in% to_scale)])
  df_outcome <- df_for_clustering %>%
    select_(.dots = resp) %>%
    na.omit()
  set.seed(9)
  clustered_df_out <- kmeans(x = df_preds, centers = n_centers, trace = FALSE)
  clustered_df <- as_tibble(data.frame(
    cluster_assignment = factor(clustered_df_out$cluster),
    df_outcome, df_preds,
    df_for_clustering %>% select(abv, ibu, srm)))
  return(clustered_df)
}

Cluster

First we’ll run the fuction with 10 centers, and cluster on the predictors ABV, IBU, SRM, total_hops, and total_malt.

cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")
clustered_beer <- cluster_it(df = beer_totals,
                             preds = cluster_on,
                             to_scale = to_scale,
                             resp = response_vars,
                             n_centers = 10)

Head of the resulting clustered data. Cluster assignment column on the far left.

kable(clustered_beer[1:20, ])

cluster_assignment	name	style	style_collapsed	abv_scaled	ibu_scaled	srm_scaled	total_hops	total_malt	abv	ibu	srm
10	"Admiral" Stache	Baltic-Style Porter	Porter	0.2700989	-0.7075654	2.1858706	0.4674779	1.1440890	7.0	23.0	37
10	"Ah Me Joy" Porter	Robust Porter	Porter	-0.6074754	0.3844558	2.4677869	-0.1933839	-0.2023226	5.4	51.0	40
6	"Bison Eye Rye" Pale Ale \| 2 of 4 Part Pale Ale Series	American-Style Pale Ale	Pale Ale	-0.3880818	0.3844558	-0.5393202	-0.1933839	-0.2023226	5.8	51.0	8
6	"Dust Up" Cloudy Pale Ale \| 1 of 4 Part Pale Ale Series	American-Style Pale Ale	Pale Ale	-0.6074754	0.5014580	-0.2574039	-0.1933839	-0.2023226	5.4	54.0	11
3	"God Country" Kolsch	German-Style Kölsch / Köln-Style Kölsch	Kölsch	-0.4977786	-0.5047614	-0.8212365	-0.1933839	-0.2023226	5.6	28.2	5
3	"Jemez Field Notes" Golden Lager	Golden or Blonde Ale	Blonde	-0.8817174	-0.8245676	-0.8212365	-0.1933839	-0.2023226	4.9	20.0	5
3	#10 Hefewiezen	South German-Style Hefeweizen / Hefeweissbier	Wheat	-0.7720206	-1.1755744	-0.9152086	-0.1933839	-0.2023226	5.1	11.0	4
3	#9	American-Style Pale Ale	Pale Ale	-0.7720206	-0.8245676	-0.4453481	0.4674779	0.4708832	5.1	20.0	9
3	#KoLSCH	German-Style Kölsch / Köln-Style Kölsch	Kölsch	-0.9365658	-0.5515624	-1.0091807	-0.1933839	-0.2023226	4.8	27.0	3
3	'Inappropriate' Cream Ale	American-Style Cream Ale or Lager	Lager	-0.6623238	-0.9025691	-0.8212365	-0.1933839	-0.2023226	5.3	18.0	5
8	'tis the Saison	French & Belgian-Style Saison	Saison	0.2700989	-0.4345601	-0.6332923	-0.1933839	-0.2023226	7.0	30.0	7
3	(306) URBAN WHEAT BEER	Belgian-Style White (or Wit) / Belgian-Style Wheat	Wheat	-0.8268690	-0.8245676	-0.4453481	-0.1933839	-0.2023226	5.0	20.0	9
4	(512) Bruin (A.K.A. Brown Bear)	American-Style Brown Ale	Brown	0.5991893	-0.4345601	0.6823171	0.1370470	1.1440890	7.6	30.0	21
8	(512) FOUR	Strong Ale	Strong Ale	0.5443409	-0.2395563	-0.5393202	0.7979088	1.1440890	7.5	35.0	8
7	(512) IPA	American-Style India Pale Ale	India Pale Ale	0.2700989	0.9304663	-0.5393202	0.7979088	0.8074861	7.0	65.0	8
8	(512) ONE	Belgian-Style Pale Strong Ale	Strong Ale	0.8185829	-0.7465661	-0.5393202	-0.1933839	0.4708832	8.0	22.0	8
6	(512) Pale	American-Style Pale Ale	Pale Ale	-0.2783850	-0.4345601	-0.6332923	0.7979088	0.8074861	6.0	30.0	7
10	(512) SIX	Belgian-Style Dubbel	Dubbel	0.5443409	-0.6295639	1.3401218	0.4674779	0.8074861	7.5	25.0	28
8	(512) THREE	Belgian-Style Tripel	Tripel	1.6413088	-0.7465661	-0.3513760	0.1370470	0.8074861	9.5	22.0	10
9	(512) THREE (Cabernet Barrel Aged)	Belgian-Style Tripel	Tripel	1.6413088	-0.7465661	2.4677869	-0.1933839	-0.2023226	9.5	22.0	40

# How many rows do we have?
nrow(clustered_beer)

[1] 3918

Join the clustered beer on beer_ingredients_join

beer_ingredients_join_clustered <- left_join(beer_ingredients_join, clustered_beer, 
                                             by = "name")

A table of cluster counts broken down by style

cluster_table_counts <- table(style = clustered_beer$style_collapsed, cluster = clustered_beer$cluster_assignment)
kable(cluster_table_counts)

	1	2	3	4	5	6	7	8	9	10
Barley Wine	0	28	0	0	14	0	2	7	11	0
Barrel-Aged	0	3	2	4	6	3	1	11	15	3
Bitter	0	0	17	20	0	38	2	1	1	1
Black	0	0	0	1	18	0	7	0	0	17
Blonde	0	0	118	2	0	13	1	24	1	1
Brown	0	1	8	95	3	2	6	0	6	27
Double India Pale Ale	0	171	0	0	11	0	45	4	1	0
Dubbel	0	0	0	16	0	0	1	7	6	11
Fruit Beer	0	0	36	7	0	2	4	4	2	1
Fruit Cider	0	0	1	0	0	0	0	0	0	0
German-Style Doppelbock	0	0	0	5	1	0	0	5	12	6
German-Style Märzen	11	0	8	10	0	1	0	0	0	0
Herb and Spice Beer	0	0	13	13	0	4	6	3	4	12
India Pale Ale	15	18	6	7	10	100	413	3	0	5
Kölsch	0	0	67	1	0	3	1	0	0	0
Lager	0	3	135	50	4	28	27	10	3	7
Other Belgian-Style Ales	0	0	4	7	1	4	9	4	5	5
Pale Ale	19	2	57	25	3	229	49	11	1	2
Pilsener	0	1	74	0	1	54	3	3	0	0
Porter	0	0	0	36	9	1	0	1	10	127
Pumpkin Beer	0	0	7	18	0	2	0	9	5	5
Red	0	8	33	125	13	46	21	7	4	16
Saison	0	0	52	6	1	34	2	41	0	3
Scotch Ale	0	0	0	10	1	0	0	5	7	10
Sour	0	0	18	4	0	3	1	4	5	2
Specialty Beer	0	1	15	13	0	5	5	11	5	10
Stout	0	0	2	6	49	2	1	3	14	126
Strong Ale	0	4	0	5	1	2	5	29	33	3
Tripel	0	2	0	0	1	1	0	57	4	0
Wheat	0	0	268	12	0	17	4	11	2	3

Plot the clusters. There are 3 axes: ABV, IBU, and SRM, so we choose two at a time.

clustered_beer_plot_abv_ibu <- ggplot(data = clustered_beer, aes(x = abv, y = ibu, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_ibu

clustered_beer_plot_abv_srm <- ggplot(data = clustered_beer, aes(x = abv, y = srm, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "SRM") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_srm

Now we can add in the style centers (means) for each style_collapsed and label it.

library(ggrepel)
abv_ibu_clusters_vs_style_centers <- ggplot() +   
  geom_point(data = clustered_beer, 
             aes(x = abv, y = ibu, colour = cluster_assignment), alpha = 0.5) +
  geom_point(data = style_centers,
             aes(mean_abv, mean_ibu), colour = "black") +
  geom_text_repel(data = style_centers, aes(mean_abv, mean_ibu, label = style_collapsed), 
                  box.padding = unit(0.45, "lines"),
                  family = "Calibri",
                  label.size = 0.3) +
  ggtitle("Popular Styles vs. k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment") +
  theme_bw()
abv_ibu_clusters_vs_style_centers

The clustering above used a smaller number of clusters (10) than there are styles_collapsed. That makes it difficult to determine whether a given style fits snugly into a cluster or not.

Cluster on just certain selected styles

We’ll take five very distinct collapsed styles and re-run the clustering on beers that fall into these categories. These styles were intentionally chosen because they are quite distinct: Blonde, IPA, Stout, Tripel, Wheat. Arguably, of these five styles Blondes and Wheats are the closest

styles_to_keep <- c("Blonde", "India Pale Ale", "Stout", "Tripel", "Wheat")
bt_certain_styles <- beer_totals %>%
  filter(
    style_collapsed %in% styles_to_keep
  ) %>% 
  droplevels()
cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")
certain_styles_clustered <- cluster_it(df = bt_certain_styles,
                                 preds = cluster_on,
                                 to_scale = to_scale,
                                 resp = response_vars,
                                 n_centers = 5)
style_centers_certain_styles <- style_centers %>% 
  filter(style_collapsed %in% styles_to_keep)

Table of style vs. cluster.

kable(table(style = certain_styles_clustered$style_collapsed, cluster = certain_styles_clustered$cluster_assignment))

Now that we have a manageable number of styles, we can see how well fit each cluster is to each style. If the features we clustered on perfectly predicted style, there would each color (cluster) would be unique to each facet of the plot. (E.g., left entirely blue, second from left entirely green, etc.)

by_style_plot <- ggplot() +   
  geom_point(data = certain_styles_clustered, 
             aes(x = abv, y = ibu,
                 colour = cluster_assignment), alpha = 0.5) +
  facet_grid(. ~ style_collapsed) +
  geom_point(data = style_centers_certain_styles,
           aes(mean_abv, mean_ibu), colour = "black", shape = 5) +
  ggtitle("Selected Styles Cluster Assignment") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster") +
  theme_bw()
by_style_plot

–>

Random asides into hops

Do more hops always mean more bitterness?

It would appear so, from this graph (considering only beer in the most popular styles) and this regression (beta = 2.394418)

ggplot(data = beer_ingredients_join, aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") + 
  ggtitle("Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

Regressing total number of hops on bitterness (IBU):

hops_ibu_lm <- lm(ibu ~ total_hops, data = beer_ingredients_join)
summary(hops_ibu_lm)

However, past a certain point (3 hops or more), there’s no effect of number of hops on IBU

ggplot(data = beer_ingredients_join[which(beer_ingredients_join$total_hops > 2
                                          & beer_ingredients_join$total_hops < 8), ], aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") +
  ggtitle("3+ Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

Most popular hops

# Gather up all the hops columns into one called `hop_name`
beer_necessities_hops_gathered <- beer_necessities %>%
  gather(
    hop_key, hop_name, hops_name_1:hops_name_13
  ) %>% as_tibble()

# Filter to just those beers that have at least one hop
beer_necessities_w_hops <- beer_necessities_hops_gathered %>% 
  filter(!is.na(hop_name)) %>% 
  filter(!hop_name == "")

beer_necessities_w_hops$hop_name <- factor(beer_necessities_w_hops$hop_name)

# For all hops, find the number of beers they're in as well as those beers' mean IBU and ABV
hops_beer_stats <- beer_necessities_w_hops %>% 
  ungroup() %>% 
  group_by(hop_name) %>% 
  summarise(
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_abv = mean(abv, na.rm = TRUE),
    n = n()
  )

# Pare to hops that are used in at least 50 beers
pop_hops_beer_stats <- hops_beer_stats[hops_beer_stats$n > 50, ]
kable(pop_hops_beer_stats)

# Keep just beers that contain these most popular hops
beer_necessities_w_popular_hops <- beer_necessities_w_hops %>% 
  filter(hop_name %in% pop_hops_beer_stats$hop_name) %>% 
  droplevels()

Are there certian hops that are used more often in very high IBU or ABV beers? Hard to detect a pattern

ggplot(data = beer_necessities_w_popular_hops) + 
  geom_point(aes(abv, ibu, colour = hop_name)) +
  ggtitle("Beers Containing most Popular Hops") +
  labs(x = "ABV", y = "IBU", colour = "Hop Name") +
  theme_minimal()

ggplot(data = pop_hops_beer_stats) + 
  geom_point(aes(mean_abv, mean_ibu, colour = hop_name, size = n)) +
  ggtitle("Most Popular Hops' Effect on Alcohol and Bitterness") +
  labs(x = "Mean ABV per Hop Type", y = "Mean IBU per Hop Type", colour = "Hop Name", 
       size = "Number of Beers") +
  theme_minimal()

Neural Net

Can ABV, IBU, and SRM be used in a neural net to predict style or style_collapsed?
In the function, specify the dataframe and the outcome, either style or style_collapsed; the one not specified as outcome will be dropped
The predictor columns will be everything not specified in the vector predictor_vars
The function returns the outcome variable sleected, neural net output, variable importance, the prediction dataframe, predictions, and accuracy


library(nnet)
library(caret)

run_neural_net <- function(df, outcome, predictor_vars) {
  out <- list(outcome = outcome)
  
  # Create a new column outcome; it's style_collapsed if you set outcome to style_collapsed, and style otherwise
  if (outcome == "style_collapsed") {
    df[["outcome"]] <- df[["style_collapsed"]]
  } else {
    df[["outcome"]] <- df[["style"]]
  }

  df$outcome <- factor(df$outcome)
  
  cols_to_keep <- c("outcome", predictor_vars)
  
  df <- df %>%
    select_(.dots = cols_to_keep) %>%
    mutate(row = 1:nrow(df)) %>% 
    droplevels()

  # Select 80% of the data for training
  df_train <- sample_n(df, nrow(df)*(0.8))
  
  # The rest is for testing
  df_test <- df %>%
    filter(! (row %in% df_train$row)) %>%
    select(-row)
  
  df_train <- df_train %>%
    select(-row)
  
  # Build multinomail neural net
  nn <- multinom(outcome ~ .,
                 data = df_train, maxit=500, trace=FALSE)

  # Which variables are the most important in the neural net?
  most_important_vars <- varImp(nn)

  # How accurate is the model? Compare predictions to outcomes from test data
  nn_preds <- predict(nn, type="class", newdata = df_test)
  nn_accuracy <- postResample(df_test$outcome, nn_preds)

  out <- list(out, nn = nn, most_important_vars = most_important_vars,
              df_test = df_test,
              nn_preds = nn_preds,
           nn_accuracy = nn_accuracy)

  return(out)
}

Set the dataframe to be beer_totals, the predictor variables to be the vector contained in p_vars, the outcome to be style_collapsed

Take out NAs

bt_omit <- beer_totals %>% na.omit()

p_vars <- c("total_hops", "total_malt", "abv", "ibu", "srm")

nn_collapsed_out <- run_neural_net(df = bt_omit, outcome = "style_collapsed", 
                         predictor_vars = p_vars)


# How accurate was it?
nn_collapsed_out$nn_accuracy

# What were the most important variables?
nn_collapsed_out$most_important_vars

What if we predcit style instead of style_collapsed?


nn_notcollapsed_out <- run_neural_net(df = bt_omit, outcome = "style", 
                         predictor_vars = p_vars)

nn_notcollapsed_out$nn_accuracy

nn_notcollapsed_out$most_important_vars

And now if we add glass as a predictor?


p_vars_add_glass <- c("total_hops", "total_malt", "abv", "ibu", "srm", "glass")

nn_collapsed_out_add_glass <- run_neural_net(df = beer_ingredients_join, outcome = "style_collapsed", 
                         predictor_vars = p_vars_add_glass)

nn_collapsed_out_add_glass$nn_accuracy

nn_collapsed_out_add_glass$most_important_vars

Random forest with all ingredients

We can use a random forest to get even more granular with ingredients
- The sparse ingredient dataframe was too complex for the multinomial neural net but the ranger can handle sparse data like this
Here we don’t include glass as a predictor


library(ranger)
library(stringr)

bi <- beer_ingredients_join %>% 
  select(-c(id, name, style, hops_name, malt_name,
            # description,
            glass)) %>% 
  mutate(row = 1:nrow(.)) %>% 
  na.omit()

bi$style_collapsed <- factor(bi$style_collapsed)


# ranger complains about special characters and spaces in ingredient column names. Take them out and replace with empty string.
names(bi) <- tolower(names(bi))
names(bi) <- str_replace_all(names(bi), " ", "")
names(bi) <- str_replace_all(names(bi), "([\\(\\)-\\/')]+)", "")

# Keep 80% for training
bi_train <- sample_n(bi, nrow(bi)*(0.8))

# The rest is for testing
bi_test <- bi %>%
  filter(! (row %in% bi_train$row)) %>%
  dplyr::select(-row)

bi_train <- bi_train %>%
  dplyr::select(-row) %>% 
  select(-`#06300`)

bi_rf <- ranger(style_collapsed ~ ., data = bi_train, importance = "impurity", seed = 11)

OOB (out of bag) prediction error is around 58% * This calculated from tree samples constructed but not used in training set; these trees become effectively part of test set

bi_rf

We can compare predicted classification on the test set to their actual style classification.

pred_bi_rf <- predict(bi_rf, dat = bi_test)
# kable(table(bi_test$style_collapsed, pred_bi_rf$predictions))

Variable importance

Interestingly, ABV, IBU, and SRM are all much more important in the random forest than total_hops and total_malt


importance(bi_rf)[1:10]

How does a CSRF (case-specific random forest) fare?


bi_csrf <- csrf(style_collapsed ~ ., training_data = bi_train, test_data = bi_test,
                params1 = list(num.trees = 5, mtry = 4),
                params2 = list(num.trees = 2))

csrf_acc <- postResample(bi_csrf, bi_test$style_collapsed)

csrf_acc

Final Thoughts

Style first, forgiveness later?

One reason seems that beers are generally brewed with style in mind first (“let’s make a pale ale”) rather than deciding the beer’s style after determining its characteristics and idiosyncrasies
- Even if the beer turns out more like a sour, and in a blind taste test might be classified as a sour more often than a pale ale, it still gets the label pale ale
- This makes the style definitions broader and harder to predict

Future Directions

Hierarchical clustering
Incorporate flavor profiles for beers sourced/scraped from somewhere
Implement a GAN to come up with beer names
More on the hops deep dive: which hops are used most often in which styles?

sessionInfo()

---
title: Data Science Musings on Beer
author:
  name: Amanda Dobbyn
date: '`r format(Sys.time(), "%B %d, %Y")`'
# output:
#   html_notebook:
#     toc: false
#     theme: yeti
#   pdf_document:
#     keep_tex: true
#     toc: false
#   github_document:
#     toc: true
    
output:
  html_document:
    keep_md: true
    toc: false
    theme: yeti
  github_document:
    toc: true
---

```{r, eval=FALSE, echo=FALSE}
# If need to close all connections
lapply( dbListConnections( dbDriver( drv = "MySQL")), dbDisconnect)
```

```{r setup, include=FALSE}
library(knitr)

# knitr::opts_knit$set(root.dir=normalizePath('../'))
knitr::opts_chunk$set(echo = FALSE, warning = FALSE)
knitr::opts_chunk$set(fig.width=12, fig.height=8) 
options(knitr.table.format = 'markdown')
```

```{r, echo=TRUE, message=FALSE}
source("./read_from_db.R")
```


This is a first pass exploration of different aspects of beer. The data was collected via the [BreweryDB](http://www.brewerydb.com/developers) API. Special thanks to [Kris Kroski](https://kro.ski/) for data ideation and co-membership in the honourable workplace beer consortium.

The main question this analysis is meant to tackle is: Are beer styles actually indicative of shared attributes of the beers within that style? Or are style boundaries more or less arbitrary? I took two approaches to this: unsupervised clustering and supervised prediction. 

Clusters defined by the algorithm were compared to the style "centers" as defined by the mean ABV, IBU, and SRM. On the prediction side, predictor variables for include ABV (alcohol by volume), IBU (international bitterness units), SRM ([a measure of color](http://www.twobeerdudes.com/beer/srm)) as well as ingredients like hops and malts. The outcome variable is the style that beer was assigned.

This document starts off with an explanation of how I sourced beer data from BreweryDB, cleaned that data, and stuck the parts of it I wanted in a database. (These are just the highlights; the code actually executed in this document queries that database, specifically by sourcing the file `read_from_db.R`, also in this repo, rather than hitting the BreweryDB API. This is done for expediency's sake as the code below detailing how to actually get the beer data, run in full in `run_it.R`, takes some time to execute.)

It then moves into clustering (k-means) and prediction (neural net, random forest).
        
The answer thus far seems to be that the beer landscape is more of a spectrum than a collection of neatly differentiated styles. Beer-intrinsic attributes like bitterness aren't great predictors of style. The relative importance of different variables depeends on the prediction method used. However, one style-defined attribute, the glass a beer is served in, increased the accuracy of prediction substantially.

Of course, other important aspects of the flavor, body, smell, etc. of the beers could not be considered because this data is not available from BreweryDB.

![](./taps.jpg)



### Workflow Overview

**Get and Prepare**

When we first hit the BreweryDB API to iteratively pull in all beers and their ingredients along with other things we might want like breweries and glassware. Then we unnest the JSON responses, including all the ingredients columns, and dump this all into a MySQL database.

Next, we create a `style_collapsed` column to reduce the number of levels of our outcome variable. We do this by `grep`ing through each beer's style to determine if that style contains a keyword that qualifies it to be rolled into a collapsed style; if it does, it gets that keyword in a `style_collapsed` column.

Finally we unnest the ingredients `hops` and `malts` into a wide, sparse dataframe. Individual ingredients are now columns, with each beer still in its own rows; a cell gets a 1 if ingredient is present and 0 otherwise. This allows more granual inference into ingredients' effects on both style and bitterness (occasioning a short foray into hops).

**Short foray into hops**

A quick look at the most popular hops and an exploration of the relationship between hops and bitterness.


**Infer**

Cluster: unsupervised k-means clustering partitioning the entire dataset into ten clusters. Next, we cluster on a dataset composed of just five selected styles into five clusters. 

We then attempt to predict predict either `style` or `style_collapsed` using a neural net and a random forest. The main predictors are ABV, IBU, SRM, total number of hops, and total number of malts. The glass a beer is served in is also considered. Finally, 

***

**Short Aside**

The question of what should be a predictor variable for style is a bit murky here. What should be fair game for predicting style and what shouldn't? Characteristics of a beer that are defined *by* its style would seem to be "cheating" in a way. The only "inputs" to a beer we have in our dataset are its ingredients, primarly hops and malts. While these certainly have an effect on its flavor profile, I consider them semi-cheating because if style is determined beforehand it likely determines at least in part which ingredients are added. The main candidates in my mind are ABV, IBU, and SRM. These are "outputs" of a beer (in the sense that they can only be exactly determined once a beer is brewered) that meaningfully define it. While correlated ABV is correlated with both IBU and SRM, the three are theoretically orthogonal to each other. A style-defined attribute like glass type is a bad candidate for a predictor variable because it is completely decoupled from the beer itself and determined entirely by the style the beer has been assigned to.




### Get and Prepare Data

**Getting beer, the age-old dilemma**

* The BreweryDB API returns a certain number of results per page; if we want 
* So, we hit the BreweryDB API and ask for `1:number_of_pages`
    * We can change `number_of_pages` to, e.g., 3 if we only want the first 3 pages
    * If there's only one page (as is the case for the glassware endpoint), numberOfPages won't be returned, so in this case we set number_of_pages to 1
* The `addition` parameter can be an empty string if nothing else is needed

```{r, eval = FALSE, echo=TRUE}

base_url <- "http://api.brewerydb.com/v2"
key_preface <- "/?key="

paginated_request <- function(ep, addition, trace_progress = TRUE) {    
  full_request <- NULL
  first_page <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                , "&p=1"))
  number_of_pages <- ifelse(!(is.null(first_page$numberOfPages)), 
                            first_page$numberOfPages, 1)      

    for (page in 1:number_of_pages) {                               
    this_request <- fromJSON(paste0(base_url, "/", ep, "/", key_preface, key
                                    , "&p=", page, addition),
                             flatten = TRUE) 
    this_req_unnested <- unnest_it(this_request)    #  <- request unnested here
    if(trace_progress == TRUE) {message(paste0("Page ", this_req_unnested$currentPage))}
    full_request <- bind_rows(full_request, this_req_unnested[["data"]])
  }
  return(full_request)
} 

all_beer_raw <- paginated_request("beers", "&withIngredients=Y")
```



* Function for unnesting JSON used inside `paginated_request()` below
    + Takes the column named `name` nested within a column in the data portion of the response
        + If the `name` column doesn't exist, it takes the first nested column
* We use something similar to unnest ingredient like all of a beer's hops and malts into a long string contained in `hops_name` and `malt_name`

```{r, eval=FALSE, echo=TRUE}
unnest_it <- function(df) {
  unnested <- df
  for(col in seq_along(df[["data"]])) {
    if(! is.null(ncol(df[["data"]][[col]]))) {
      if(! is.null(df[["data"]][[col]][["name"]])) {
        unnested[["data"]][[col]] <- df[["data"]][[col]][["name"]]
      } else {
        unnested[["data"]][[col]] <- df[["data"]][[col]][[1]]
      }
    }
  }
  return(unnested)
}
```



**Collapse Styles**

* Save the most popular styles in `keywords`
* Loop through each keyword
    * For each beer, `grep` through its style column to see if it contains any one of these keywords
    * If it does, give it that keyword in a new column `style_collapsed`
* If a beer's name matches multiple keywords, e.g., American Double India Pale Ale would match Double India Pale Ale, India Pale Ale, and Pale Ale, its `style_collapsed` is the **last** of those that appear in keywords 
    * This is why keywords are intentionally ordered from most general to most specific
    * So in the case of an case of American Double India Pale Ale: since Double India Pale Ale appears in `keywords` after India Pale Ale and Pale Ale, an American Double India Pale Ale would get a `style_collapsed` of Double India Pale Ale
* If no keyword is contained in `style`, `style_collapsed` is just whatever's in `style`; in other words, it doesn't get collpsed into a bigger bucket
    * This isn't a huge problem because we'll pare down to just the most popular styles later, however we could think about creating a catchall "Other" level for `style_collapsed`

```{r, eval=FALSE, echo=TRUE}


keywords <- c("Lager", "Pale Ale", "India Pale Ale", "Double India Pale Ale", "India Pale Lager", "Hefeweizen", "Barrel-Aged","Wheat", "Pilsner", "Pilsener", "Amber", "Golden", "Blonde", "Brown", "Black", "Stout", "Porter", "Red", "Sour", "Kölsch", "Tripel", "Bitter", "Saison", "Strong Ale", "Barley Wine", "Dubbel", "Altbier")

collapse_styles <- function(df, trace_progress = TRUE) {
  
  df[["style_collapsed"]] <- vector(length = nrow(df))
  
  for (beer in 1:nrow(df)) {
    if (grepl(paste(keywords, collapse="|"), df$style[beer])) {    
      for (keyword in keywords) {         
        if(grepl(keyword, df$style[beer]) == TRUE) {
          df$style_collapsed[beer] <- keyword    
        }                         
      } 
    } else {
      df$style_collapsed[beer] <- as.character(df$style[beer])       
    }
    if(trace_progress == TRUE) {message(paste0("Collapsing this ", df$style[beer], " to: ", df$style_collapsed[beer]))}
  }
  return(df)
}

```

* Then we collapse further; right now we just combine all wheaty bears into Wheat and Pils-like beers into Pilsener (with two e's) by `fct_collapse`ing those levels

```{r, echo=TRUE, eval=FALSE}
collapse_further <- function(df) {
  df[["style_collapsed"]] <- df[["style_collapsed"]] %>%
    fct_collapse(
      "Wheat" = c("Hefeweizen", "Wheat"),
      "Pilsener" = c("Pilsner", "American-Style Pilsener") # pilsener == pilsner == pils
    )
  return(df)
}
```



**Split out Ingredients**

When we unnested ingredients, we just concatenated all of the ingredients for a given beer into a long string. If we want, we can split out the ingredients that were concatenated in `<ingredient>_name` with this `split_ingredients` function.

This takes a vector of `ingredients_to_split`, so e.g. `c("hops_name", "malt_name")` and creates one column for each type of ingredient (`hops_name_1`, `hops_name_2`, etc.). It's flexible enough to adapt if data in BreweryDB changes and a beer now has 15 hops where before the maximum number of hops a beer had was 10.

```{r, eval=FALSE, echo=TRUE}
split_ingredients <- function(df, ingredients_to_split) {
  
  ncol_df <- ncol(df)
  
  for (ingredient in ingredients_to_split) {

    ingredient_split <- str_split(df[[ingredient]], ", ")    
    num_new_cols <- max(lengths(ingredient_split))    
  
    for (num in 1:num_new_cols) {
      
      this_col <- ncol_df + 1         
      
      df[, this_col] <- NA
      names(df)[this_col] <- paste0(ingredient, "_", num)
      ncol_df <- ncol(df)             
      for (row in seq_along(ingredient_split)) {          
        if (!is.null(ingredient_split[[row]][num])) {        
          df[row, this_col] <- ingredient_split[[row]][num]
        }
      }
      df[[names(df)[this_col]]] <- factor(df[[names(df)[this_col]]])
    }
    
    ncol_df <- ncol(df)
  }
  return(df)
}
```


Some quick summary stats on our main dataframe called `beer_necessities`:
```{r, echo=TRUE}
dim(beer_necessities)
str(beer_necessities)
```


**Find the Most Popualar Styles**

We find mean ABV, IBU, and SRM per collapsed style and arrange collapsed styles by the number of beers that fall into them. (This is of course dependent on how we collapse styles; if we looped all Double IPAs in with IPAs then the category IPA would be much bigger than it is if we keep the two separate.)

```{r, eval=TRUE, echo=TRUE}
library(forcats)

# Pare down to only cases where style is not NA
beer_dat_pared <- beer_necessities[complete.cases(beer_necessities$style), ]

# Arrange beer dat by style popularity
style_popularity <- beer_dat_pared %>% 
  group_by(style) %>% 
  count() %>% 
  arrange(desc(n))

# Add a column that scales popularity
style_popularity <- bind_cols(style_popularity, 
                               n_scaled = as.vector(scale(style_popularity$n)))

# Find styles that are above a z-score of 0
popular_styles <- style_popularity %>% 
  filter(n_scaled > 0)

# Pare dat down to only beers that fall into those styles
popular_beer_dat <- beer_dat_pared %>% 
  filter(
    style %in% popular_styles$style
  ) %>% 
  droplevels() %>% 
  as_tibble() 
```


How many rows do we have in our dataset of just beers that fall into the popular styles?
```{r, echo=TRUE}
nrow(popular_beer_dat)
```


Now we find the style centers.
```{r, echo=TRUE}
# Find the centers (mean abv, ibu, srm) of the most popular styles
style_centers <- popular_beer_dat %>% 
  group_by(style_collapsed) %>% 
  add_count() %>% 
  summarise(
    mean_abv = mean(abv, na.rm = TRUE),
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_srm = mean(srm, na.rm = TRUE),
    n = median(n, na.rm = TRUE)          # Median here only for summarise. Should be just the same as n
  ) %>% 
  arrange(desc(n)) %>% 
  drop_na() %>% 
  droplevels()

# Give some nicer names
style_centers_rename <- style_centers %>% 
  rename(
    `Collapsed Style` = style_collapsed,
    `Mean ABV` = mean_abv,
    `Mean IBU` = mean_ibu,
    `Mean SRM` = mean_srm,
    `Numer of Beers` = n
  )
```


Take a look at the table, ordered by number of beers in that style, descending.      

```{r}
kable(style_centers_rename)
```



***

### Ingredients

To get more granular with ingredients, we can split out each individual ingredient into its own column. If a beer or style contains that ingredient, its row gets a 1 in that ingredient column and a 0 otherwise.

From this, we can find the total number of hops and malts per grouper.

* The dataframe we'll use will be `beer_necessities`



* This function takes a dataframe and two other parameters set at the outset:
    * `ingredient_want`: this can be `hops`, `malt`, or other ingredients like `yeast` if we pull that in
    * `grouper`: can be a vector of one or more things to group by, like beer `name` or `style`

```{r, eval=TRUE, echo=TRUE}

pick_ingredient_get_beer <- function (ingredient_want, df, grouper) {
  
  # ----------------------- Setup --------------------------- #
  # We've already split ingredient number names out from the concatenated string into columns like `malt_name_1`,
  # `malt_name_2`, etc. We need to find the range of these columns; there will be a different number of malt
  # columns than hops columns, for instance. The first one will be `<ingredient>_name_1` and from this we can find
  # the index of this column in our dataframe. We get the name of last one with the `get_last_ing_name_col()`
  # function. Then we save a vector of all the ingredient column names in `ingredient_colnames`. It will stay
  # constant even if the indices change when we select out certain columns. 
  
  # First ingredient
  first_ingredient_name <- paste(ingredient_want, "_name_1", sep="")
  first_ingredient_index <- which(colnames(df)==first_ingredient_name)
  
  # Get the last ingredient
  get_last_ing_name_col <- function(df) {
    for (col in names(df)) {
      if (grepl(paste(ingredient_want, "_name_", sep = ""), col) == TRUE) {
        name_last_ing_col <- col
      }
    }
    return(name_last_ing_col)
  }
  
  # Last ingredient
  last_ingredient_name <- get_last_ing_name_col(df)
  last_ingredient_index <- which(colnames(df)==last_ingredient_name)
  
  # Vector of all the ingredient column names
  ingredient_colnames <- names(df)[first_ingredient_index:last_ingredient_index]
  
  # Non-ingredient column names we want to keep
  to_keep_col_names <- c("id", "cluster_assignment", "name", "abv", "ibu", "srm", "style", "style_collapsed")
  
  # -------------------------------------------------------------------------------# 
  
  # Inside `gather_ingredients()` we take out superflous column names that are not in `to_keep_col_names` or one 
  # of the ingredient columns, find what the new ingredient column indices are, since they'll have changed after 
  # we pared down and then gather all of the ingredient columns (e.g., `hops_name_1`) into one long column, 
  # `ing_keys` and all the actual ingredient names (e.g., Cascade) into `ing_names`.
  
  # ----------------------------- Gather columns --------------------------------- #
  gather_ingredients <- function(df, cols_to_gather) {
    to_keep_indices <- which(colnames(df) %in% to_keep_col_names)
    
    selected_df <- df[, c(to_keep_indices, first_ingredient_index:last_ingredient_index)]
    
    new_ing_indices <- which(colnames(selected_df) %in% cols_to_gather)    # indices will have changed since we pared down 
    
    df_gathered <- selected_df %>%
      gather_(
        key_col = "ing_keys",
        value_col = "ing_names",
        gather_cols = colnames(selected_df)[new_ing_indices]
      ) %>%
      mutate(
        count = 1
      )
    return(df_gathered)
  }
  beer_gathered <- gather_ingredients(df, ingredient_colnames)  # ingredient colnames defined above function
  # ------------------------------------------------------------------------------- # 
  
  # Next we get a vector of all ingredient levels and take out the one that's an empty string and 
  # use this vector of ingredient levels in `select_spread_cols()` below

  # Get a vector of all ingredient levels
  beer_gathered$ing_names <- factor(beer_gathered$ing_names)
  ingredient_levels <- levels(beer_gathered$ing_names) 
  
  # Take out the level that's just an empty string
  to_keep_levels <- !(c(1:length(ingredient_levels)) %in% which(ingredient_levels == ""))
  ingredient_levels <- ingredient_levels[to_keep_levels]
  
  beer_gathered$ing_names <- as.character(beer_gathered$ing_names)
  
  # ----------------------------------------------------------------------------- # 
  
  # Then we spread the ingredient names: we take what was previously the `value` in our gathered dataframe, the
  # actual ingredient names (Cascade, Centennial) and make that our `key`; it'll form the new column names. The
  # new `value` is `value` is count; it'll populate the row cells. If a given row has a certain ingredient, it
  # gets a 1 in the corresponding cell, an NA otherwise. 
  # We add a unique idenfitier for each row with `row`, which we'll drop later (see [Hadley's SO
  # comment](https://stackoverflow.com/questions/25960394/unexpected-behavior-with-tidyr)).

  
  # ------------------------------- Spread columns -------------------------------- #
  spread_ingredients <- function(df) {
    df_spread <- df %>% 
      mutate(
        row = 1:nrow(df)        # Add a unique idenfitier for each row which we'll need in order to spread; we'll drop this later
      ) %>%                                 
      spread(
        key = ing_names,
        value = count
      ) 
    return(df_spread)
  }
  beer_spread <- spread_ingredients(beer_gathered)
  # ------------------------------------------------------------------------------- # 

  
  # ------------------------- Select only certain columns ------------------------- #
  select_spread_cols <- function(df) {
    to_keep_col_indices <- which(colnames(df) %in% to_keep_col_names)
    to_keep_ingredient_indices <- which(colnames(df) %in% ingredient_levels)
    
    to_keep_inds_all <- c(to_keep_col_indices, to_keep_ingredient_indices)
    
    new_df <- df %>% 
      select_(
        .dots = to_keep_inds_all
      )
    return(new_df)
  }
  beer_spread_selected <- select_spread_cols(beer_spread)
  # ------------------------------------------------------------------------------- # 

  # Take out all rows that have no ingredients specified at all
  inds_to_remove <- apply(beer_spread_selected[, first_ingredient_index:last_ingredient_index], 
                          1, function(x) all(is.na(x)))
  beer_spread_no_na <- beer_spread_selected[ !inds_to_remove, ]
  
  
  # ----------------- Group ingredients by the grouper specified ------------------- #
  # Then we do the final step and group by the groupers.
  
  get_ingredients_per_grouper <- function(df, grouper = grouper) {
    df_grouped <- df %>%
      ungroup() %>% 
      group_by_(grouper)
    
    not_for_summing <- which(colnames(df_grouped) %in% to_keep_col_names)
    max_not_for_summing <- max(not_for_summing)
    
    browser()
    per_grouper <- df_grouped %>% 
      select(-c(abv, ibu, srm)) %>%    # taking out temporarily
      summarise_if(
        is.numeric,              
        sum, na.rm = TRUE
        # -c(abv, ibu, srm)
      ) %>%
      mutate(
        total = rowSums(.[(max_not_for_summing + 1):ncol(.)], na.rm = TRUE)    
      )
    
    # Send total to the second position
    per_grouper <- per_grouper %>% 
      select(
        id, total, everything()
      )
    
    # Replace total column with more descriptive name: total_<ingredient>
    names(per_grouper)[which(names(per_grouper) == "total")] <- paste0("total_", ingredient_want)
    
    return(per_grouper)
  }
  # ------------------------------------------------------------------------------- # 
  
  ingredients_per_grouper <- get_ingredients_per_grouper(beer_spread_selected, grouper)
  return(ingredients_per_grouper)
}
```


* Now run the function with `ingredient_want` as first hops, then malt
* Then join the resulting dataframes and remove/reorder some columns

```{r, echo=TRUE, eval=TRUE}
# Run the entire function with ingredient_want set to hops, grouping by name
ingredients_per_beer_hops <- pick_ingredient_get_beer(ingredient_want = "hops", 
                                                      beer_necessities, 
                                                      grouper = c("id"))

# Same for malt
ingredients_per_beer_malt <- pick_ingredient_get_beer(ingredient_want = "malt", 
                                                      beer_necessities, 
                                                      grouper = c("id"))

# Join those on our original dataframe by name
beer_ingredients_join_first_ingredient <- left_join(beer_necessities, ingredients_per_beer_hops,
                                                    by = "id")
beer_ingredients_join <- left_join(beer_ingredients_join_first_ingredient, ingredients_per_beer_malt,
                                   by = "id")


# Take out some unnecessary columns
unnecessary_cols <- c("styleId", "abv_scaled", "ibu_scaled", "srm_scaled", 
                      "hops_id", "malt_id", "glasswareId", "style.categoryId")
beer_ingredients_join <- beer_ingredients_join[, (! names(beer_ingredients_join) %in% unnecessary_cols)]


# If we also want to take out any of the malt_name_1, malt_name_2, etc. columns we can do this with a grep
more_unnecessary <- c("hops_name_|malt_name_")
beer_ingredients_join <- 
  beer_ingredients_join[, (! grepl(more_unnecessary, names(beer_ingredients_join)) == TRUE)]

# Reorder columns a bit
beer_ingredients_join_all <- beer_ingredients_join %>% 
  select(
    id, name, total_hops, total_malt, everything(), -description
  )

# Keep only beers that fall into a style_collapsed bucket
# Not filtering by levels in beer_necessities$style_collapsed because those levels contain more than what's in just the keywords of collapse_styles()
beer_ingredients_join <- beer_ingredients_join_all %>% 
  filter(
    style_collapsed %in% levels(style_centers$style_collapsed)
  ) %>% 
  droplevels()

# And get a df that includes total_hops and total_malt but not all the other ingredient columns
beer_totals_all <- beer_ingredients_join_all %>% 
  select(
    id, name, total_hops, total_malt, style, style_collapsed,
    abv, ibu, srm, glass, hops_name, malt_name
  )

# And just style_collapsed
beer_totals <- beer_ingredients_join %>% 
  filter(
    style_collapsed %in% levels(style_centers$style_collapsed)
  ) %>% 
  droplevels()


```


Now we're left with something of a sparse matrix of all the ingredients compared to all the beers
```{r}
kable(beer_ingredients_join[1:20, ])
```



***

Now that the munging is done, onto the main question: do natural clusters in beer align with style boundaries?


***

### Unsupervised Clustering 
We K-means cluster beers based on certain numeric predictor variables. 


**Prep**

* Write a funciton that takes a dataframe, a set of predictors, a response variable, and the number of cluster centers you want
    * NB: There are not not very many beers have SRM so we may not want to omit based on it

* Take out missing values, and scale the data
* Take out outliers, defined as beers have to have an ABV between 3 and 20 and an IBU less than 200
* Then cluster on just the predictors and compare to the response variable
  

```{r, echo=TRUE}

library(NbClust)

cluster_it <- function(df, preds, to_scale, resp, n_centers) {
  df_for_clustering <- df %>%
    select_(.dots = c(response_vars, cluster_on)) %>%
    na.omit() %>%
    filter(
      abv < 20 & abv > 3
    ) %>%
    filter(
      ibu < 200
    )

  df_all_preds <- df_for_clustering %>%
    select_(.dots = preds)

  df_preds_scale <- df_all_preds %>%
    select_(.dots = to_scale) %>%
    rename(
      abv_scaled = abv,
      ibu_scaled = ibu,
      srm_scaled = srm
    ) %>%
    scale() %>%
    as_tibble()

  df_preds <- bind_cols(df_preds_scale, df_all_preds[, (!names(df_all_preds) %in% to_scale)])

  df_outcome <- df_for_clustering %>%
    select_(.dots = resp) %>%
    na.omit()

  set.seed(9)
  clustered_df_out <- kmeans(x = df_preds, centers = n_centers, trace = FALSE)

  clustered_df <- as_tibble(data.frame(
    cluster_assignment = factor(clustered_df_out$cluster),
    df_outcome, df_preds,
    df_for_clustering %>% select(abv, ibu, srm)))

  return(clustered_df)
}

```



 
**Cluster**

First we'll run the fuction with 10 centers, and cluster on the predictors ABV, IBU, SRM, total_hops, and total_malt.


```{r, echo=TRUE}

cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")

clustered_beer <- cluster_it(df = beer_totals,
                             preds = cluster_on,
                             to_scale = to_scale,
                             resp = response_vars,
                             n_centers = 10)
```


Head of the resulting clustered data. Cluster assignment column on the far left.
```{r, echo=TRUE}
kable(clustered_beer[1:20, ])

# How many rows do we have?
nrow(clustered_beer)
```

Join the clustered beer on `beer_ingredients_join`
```{r}
beer_ingredients_join_clustered <- left_join(beer_ingredients_join, clustered_beer, 
                                             by = "name")
```


A table of cluster counts broken down by style
```{r}
cluster_table_counts <- table(style = clustered_beer$style_collapsed, cluster = clustered_beer$cluster_assignment)

kable(cluster_table_counts)
```


Plot the clusters. There are 3 axes: ABV, IBU, and SRM, so we choose two at a time. 

```{r, echo=TRUE}
clustered_beer_plot_abv_ibu <- ggplot(data = clustered_beer, aes(x = abv, y = ibu, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_ibu

clustered_beer_plot_abv_srm <- ggplot(data = clustered_beer, aes(x = abv, y = srm, colour = cluster_assignment)) + 
  geom_jitter() + theme_minimal()  +
  ggtitle("k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "SRM") +
  labs(colour = "Cluster Assignment")
clustered_beer_plot_abv_srm
```



Now we can add in the style centers (means) for each `style_collapsed` and label it.

```{r, echo=TRUE}
library(ggrepel)
abv_ibu_clusters_vs_style_centers <- ggplot() +   
  geom_point(data = clustered_beer, 
             aes(x = abv, y = ibu, colour = cluster_assignment), alpha = 0.5) +
  geom_point(data = style_centers,
             aes(mean_abv, mean_ibu), colour = "black") +
  geom_text_repel(data = style_centers, aes(mean_abv, mean_ibu, label = style_collapsed), 
                  box.padding = unit(0.45, "lines"),
                  family = "Calibri",
                  label.size = 0.3) +
  ggtitle("Popular Styles vs. k-Means Clustering of Beer by ABV, IBU, SRM") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster Assignment") +
  theme_bw()
abv_ibu_clusters_vs_style_centers
```


The clustering above used a smaller number of clusters (10) than there are `styles_collapsed`. That makes it difficult to determine whether a given style fits snugly into a cluster or not.



**Cluster on just certain selected styles**

We'll take five very distinct collapsed styles and re-run the clustering on beers that fall into these categories. 
These styles were intentionally chosen because they are quite distinct: Blonde, IPA, Stout, Tripel, Wheat. Arguably, of these five styles Blondes and Wheats are the closest



```{r, echo=TRUE}
styles_to_keep <- c("Blonde", "India Pale Ale", "Stout", "Tripel", "Wheat")
bt_certain_styles <- beer_totals %>%
  filter(
    style_collapsed %in% styles_to_keep
  ) %>% 
  droplevels()


cluster_on <- c("abv", "ibu", "srm", "total_hops", "total_malt")
to_scale <- c("abv", "ibu", "srm", "total_hops", "total_malt")
response_vars <- c("name", "style", "style_collapsed")

certain_styles_clustered <- cluster_it(df = bt_certain_styles,
                                 preds = cluster_on,
                                 to_scale = to_scale,
                                 resp = response_vars,
                                 n_centers = 5)

style_centers_certain_styles <- style_centers %>% 
  filter(style_collapsed %in% styles_to_keep)
```





Table of style vs. cluster.
```{r, echo=TRUE}
kable(table(style = certain_styles_clustered$style_collapsed, cluster = certain_styles_clustered$cluster_assignment))
```



Now that we have a manageable number of styles, we can see how well fit each cluster is to each style. If the features we clustered on perfectly predicted style, there would each color (cluster) would be unique to each facet of the plot. (E.g., left entirely blue, second from left entirely green, etc.)



```{r, echo=TRUE}
by_style_plot <- ggplot() +   
  geom_point(data = certain_styles_clustered, 
             aes(x = abv, y = ibu,
                 colour = cluster_assignment), alpha = 0.5) +
  facet_grid(. ~ style_collapsed) +
  geom_point(data = style_centers_certain_styles,
           aes(mean_abv, mean_ibu), colour = "black", shape = 5) +
  ggtitle("Selected Styles Cluster Assignment") +
  labs(x = "ABV", y = "IBU") +
  labs(colour = "Cluster") +
  theme_bw()
by_style_plot
```




<!-- ### Back to clustering: cluster on only 5 styles -->

<!-- * We'll pare down the beer data to just beers in 5 selected styles; 
<!-- * We'll cluster these into 5 clusters -->
<!-- <!-- * This time we'll add in `total_hops` and `total_malt` as predictors  --> -->




<!-- ggplot() + -->
<!--   geom_point(data = certain_styles_clustered, -->
<!--              aes(x = abv, y = ibu, -->
<!--                  shape = cluster_assignment, -->
<!--                  colour = style_collapsed), alpha = 0.5) + -->
<!--   geom_point(data = style_centers_certain_styles, -->
<!--              aes(mean_abv, mean_ibu), colour = "black") + -->
<!--   geom_text_repel(data = style_centers_certain_styles, -->
<!--                   aes(mean_abv, mean_ibu, label = style_collapsed), -->
<!--                   box.padding = unit(0.45, "lines"), -->
<!--                   family = "Calibri", -->
<!--                   label.size = 0.3) + -->
<!--   ggtitle("Selected Styles (colors) matched with Cluster Assignments (shapes)") + -->
<!--   labs(x = "ABV", y = "IBU") + -->
<!--   labs(colour = "Style", shape = "Cluster Assignment") + -->
<!--   theme_bw() -->

<!-- ``` -->



## Random asides into hops

**Do more hops always mean more bitterness?**

* It would appear so, from this graph (considering only beer in the most popular styles) and this regression (beta = 2.394418)
```{r, echo=TRUE}
ggplot(data = beer_ingredients_join, aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") + 
  ggtitle("Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()

```


Regressing total number of hops on bitterness (IBU):
```{r, echo = TRUE}
hops_ibu_lm <- lm(ibu ~ total_hops, data = beer_ingredients_join)
summary(hops_ibu_lm)
```


* However, past a certain point (3 hops or more), there's no effect of number of hops on IBU
```{r, echo=TRUE}
ggplot(data = beer_ingredients_join[which(beer_ingredients_join$total_hops > 2
                                          & beer_ingredients_join$total_hops < 8), ], aes(total_hops, ibu)) +
  geom_point(aes(total_hops, ibu, colour = style_collapsed)) +
  geom_smooth(method = lm, se = FALSE, colour = "black") +
  ggtitle("3+ Hops Per Beer vs. Bitterness") +
  labs(x = "Number of Hops", y = "IBU", colour = "Style Collapsed") +
  theme_minimal()
```


**Most popular hops**

```{r, echo=TRUE}
# Gather up all the hops columns into one called `hop_name`
beer_necessities_hops_gathered <- beer_necessities %>%
  gather(
    hop_key, hop_name, hops_name_1:hops_name_13
  ) %>% as_tibble()

# Filter to just those beers that have at least one hop
beer_necessities_w_hops <- beer_necessities_hops_gathered %>% 
  filter(!is.na(hop_name)) %>% 
  filter(!hop_name == "")

beer_necessities_w_hops$hop_name <- factor(beer_necessities_w_hops$hop_name)

# For all hops, find the number of beers they're in as well as those beers' mean IBU and ABV
hops_beer_stats <- beer_necessities_w_hops %>% 
  ungroup() %>% 
  group_by(hop_name) %>% 
  summarise(
    mean_ibu = mean(ibu, na.rm = TRUE), 
    mean_abv = mean(abv, na.rm = TRUE),
    n = n()
  )

# Pare to hops that are used in at least 50 beers
pop_hops_beer_stats <- hops_beer_stats[hops_beer_stats$n > 50, ]
kable(pop_hops_beer_stats)

# Keep just beers that contain these most popular hops
beer_necessities_w_popular_hops <- beer_necessities_w_hops %>% 
  filter(hop_name %in% pop_hops_beer_stats$hop_name) %>% 
  droplevels() 
```

Are there certian hops that are used more often in very high IBU or ABV beers?
Hard to detect a pattern
```{r, echo = TRUE}
ggplot(data = beer_necessities_w_popular_hops) + 
  geom_point(aes(abv, ibu, colour = hop_name)) +
  ggtitle("Beers Containing most Popular Hops") +
  labs(x = "ABV", y = "IBU", colour = "Hop Name") +
  theme_minimal()
```

```{r, echo=TRUE}
ggplot(data = pop_hops_beer_stats) + 
  geom_point(aes(mean_abv, mean_ibu, colour = hop_name, size = n)) +
  ggtitle("Most Popular Hops' Effect on Alcohol and Bitterness") +
  labs(x = "Mean ABV per Hop Type", y = "Mean IBU per Hop Type", colour = "Hop Name", 
       size = "Number of Beers") +
  theme_minimal()
```


# Neural Net

* Can ABV, IBU, and SRM be used in a neural net to predict `style` or `style_collapsed`?
* In the function, specify the dataframe and the outcome, either `style` or `style_collapsed`; the one not specified as `outcome` will be dropped
* The predictor columns will be everything not specified in the vector `predictor_vars`
* The function returns the outcome variable sleected, neural net output, variable importance, the prediction dataframe, predictions, and accuracy

```{r, warning=FALSE, echo=TRUE, eval=TRUE, message=FALSE}

library(nnet)
library(caret)

run_neural_net <- function(df, outcome, predictor_vars) {
  out <- list(outcome = outcome)
  
  # Create a new column outcome; it's style_collapsed if you set outcome to style_collapsed, and style otherwise
  if (outcome == "style_collapsed") {
    df[["outcome"]] <- df[["style_collapsed"]]
  } else {
    df[["outcome"]] <- df[["style"]]
  }

  df$outcome <- factor(df$outcome)
  
  cols_to_keep <- c("outcome", predictor_vars)
  
  df <- df %>%
    select_(.dots = cols_to_keep) %>%
    mutate(row = 1:nrow(df)) %>% 
    droplevels()

  # Select 80% of the data for training
  df_train <- sample_n(df, nrow(df)*(0.8))
  
  # The rest is for testing
  df_test <- df %>%
    filter(! (row %in% df_train$row)) %>%
    select(-row)
  
  df_train <- df_train %>%
    select(-row)
  
  # Build multinomail neural net
  nn <- multinom(outcome ~ .,
                 data = df_train, maxit=500, trace=FALSE)

  # Which variables are the most important in the neural net?
  most_important_vars <- varImp(nn)

  # How accurate is the model? Compare predictions to outcomes from test data
  nn_preds <- predict(nn, type="class", newdata = df_test)
  nn_accuracy <- postResample(df_test$outcome, nn_preds)

  out <- list(out, nn = nn, most_important_vars = most_important_vars,
              df_test = df_test,
              nn_preds = nn_preds,
           nn_accuracy = nn_accuracy)

  return(out)
}

```

* Set the dataframe to be `beer_totals`, the predictor variables to be the vector contained in `p_vars`, the outcome to be `style_collapsed`


Take out NAs
```{r, echo=TRUE}
bt_omit <- beer_totals %>% na.omit()
```

```{r, echo=TRUE, eval=TRUE, error=TRUE}
p_vars <- c("total_hops", "total_malt", "abv", "ibu", "srm")

nn_collapsed_out <- run_neural_net(df = bt_omit, outcome = "style_collapsed", 
                         predictor_vars = p_vars)


# How accurate was it?
nn_collapsed_out$nn_accuracy

# What were the most important variables?
nn_collapsed_out$most_important_vars

```


* What if we predcit `style` instead of `style_collapsed`?

```{r, echo=TRUE, error=TRUE}

nn_notcollapsed_out <- run_neural_net(df = bt_omit, outcome = "style", 
                         predictor_vars = p_vars)

nn_notcollapsed_out$nn_accuracy

nn_notcollapsed_out$most_important_vars

```


And now if we add `glass` as a predictor?
```{r, echo=TRUE, error=TRUE}

p_vars_add_glass <- c("total_hops", "total_malt", "abv", "ibu", "srm", "glass")

nn_collapsed_out_add_glass <- run_neural_net(df = beer_ingredients_join, outcome = "style_collapsed", 
                         predictor_vars = p_vars_add_glass)

nn_collapsed_out_add_glass$nn_accuracy

nn_collapsed_out_add_glass$most_important_vars

```




### Random forest with all ingredients

* We can use a random forest to get even more granular with ingredients
    * The sparse ingredient dataframe was too complex for the multinomial neural net but the `ranger` can handle sparse data like this

* Here we don't include `glass` as a predictor

```{r, echo=TRUE}

library(ranger)
library(stringr)

bi <- beer_ingredients_join %>% 
  select(-c(id, name, style, hops_name, malt_name,
            # description,
            glass)) %>% 
  mutate(row = 1:nrow(.)) %>% 
  na.omit()

bi$style_collapsed <- factor(bi$style_collapsed)


# ranger complains about special characters and spaces in ingredient column names. Take them out and replace with empty string.
names(bi) <- tolower(names(bi))
names(bi) <- str_replace_all(names(bi), " ", "")
names(bi) <- str_replace_all(names(bi), "([\\(\\)-\\/')]+)", "")

# Keep 80% for training
bi_train <- sample_n(bi, nrow(bi)*(0.8))

# The rest is for testing
bi_test <- bi %>%
  filter(! (row %in% bi_train$row)) %>%
  dplyr::select(-row)

bi_train <- bi_train %>%
  dplyr::select(-row) %>% 
  select(-`#06300`)

bi_rf <- ranger(style_collapsed ~ ., data = bi_train, importance = "impurity", seed = 11)
```


OOB (out of bag) prediction error is around 58%
    * This calculated from tree samples constructed but not used in training set; these trees become effectively part of test set
```{r}
bi_rf
```


We can compare predicted classification on the test set to their actual style classification.
```{r, echo=TRUE}
pred_bi_rf <- predict(bi_rf, dat = bi_test)
# kable(table(bi_test$style_collapsed, pred_bi_rf$predictions))
```


Variable importance

* Interestingly, ABV, IBU, and SRM are all much more important in the random forest than `total_hops` and `total_malt`
```{r, echo=TRUE}

importance(bi_rf)[1:10]
```


How does a CSRF (case-specific random forest) fare?

```{r, echo=TRUE}

bi_csrf <- csrf(style_collapsed ~ ., training_data = bi_train, test_data = bi_test,
                params1 = list(num.trees = 5, mtry = 4),
                params2 = list(num.trees = 2))

csrf_acc <- postResample(bi_csrf, bi_test$style_collapsed)

csrf_acc
```





### Final Thoughts


*Style first, forgiveness later?*

* One reason  seems that beers are generally brewed with style in mind first ("let's make a pale ale") rather than deciding the beer's style after determining its characteristics and idiosyncrasies 
    * Even if the beer turns out more like a sour, and in a blind taste test might be classified as a sour more often than a pale ale, it still gets the label pale ale
    * This makes the style definitions broader and harder to predict



*Future Directions*

* Hierarchical clustering
* Incorporate flavor profiles for beers sourced/scraped from somewhere
* Implement a GAN to come up with beer names
* More on the hops deep dive: which hops are used most often in which styles?



![](./pour.jpg)


```{r, echo=TRUE}
sessionInfo()
```





Data Science Musings on Beer

Amanda Dobbyn

July 06, 2017